[dblessing]

I replaced the tail lights with LEDs, too, and they flash correctly. This pickup does not have hazards.

I thought maybe one of the lights was leaking voltage through the ground, enough to light up the LED but not an incandescent. I turned the switch to the right and also removed the right socket and the left still flashed. So any electrical short/bad wiring is happening in the harness and not as a result of the ground, it seems. I'm not sure where to take it from here.

For completeness, I tried reversing the polarity on the flasher and it didn't work at all, so I'm reasonably confident the flasher is working correctly. And again, the new flasher works with the incandescents (and the rear tail lights).